Improved Performance Low-Cost Incremental Conductance PV ... · steady-state power oscillations and...
Transcript of Improved Performance Low-Cost Incremental Conductance PV ... · steady-state power oscillations and...
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Improved Performance Low-Cost Incremental Conductance PV MPPT Technique
N.E. Zakzouk, M.A.Elsaharty, A.K. Abdelsalam, A.A. Helal B.W. Williams
Electrical and Control Engineering Department Electronics and Electrical Engineering Department
Arab Academy for Science and Technology (AAST) Strathclyde University
Alexandria, Egypt Glasgow, United Kingdom
Abstract-Variable-step incremental conductance (Inc.Cond.) technique, for photovoltaic (PV) maximum power point
tracking (MPPT), has merits of good tracking accuracy and fast convergence speed. Yet, it lacks simplicity in its
implementation due to the mathematical division computations involved in its algorithm structure. Furthermore, the
conventional variable step-size, based on the division of the PV module power change by the PV voltage change, encounters
steady-state power oscillations and dynamic problems especially under sudden environmental changes. In this paper, an
enhancement is introduced to Inc.Cond. algorithm in order to entirely eliminate the division calculations involved in its
structure. Hence, algorithm implementation complexity is minimized enabling the utilization of low-cost microcontrollers to
cut down system cost. Moreover, the required real processing time is reduced, thus sampling rate can be improved to fasten
system response during sudden changes. Regarding the applied step-size, a modified variable-step size, which depends solely
on PV power, is proposed. The latter achieves enhanced transient performance with minimal steady-state power oscillations
around the MPP even under partial shading. For proposed technique's validation, simulation work is carried out and an
experimental set up is implemented in which ARDUINO Uno board, based on low-cost Atmega328 microcontroller, is
employed.
Keywords—PV module, MPPT, incremental conductance, variable step size, environmental changes, low-cost microcontroller, and partial
shading.
I. Introduction
The modern industrial society, population growth, and the interest in the environmental issues have greatly increased the need
of new and clean renewable energy sources [1]. Among the latter, Photovoltaic (PV) solar energy has become nowadays a real
promising renewable/ alternate energy source due to its several advantages such as; absence of noise or mechanical moving parts,
low operation cost, no emission of CO2 or other harmful gases, flexibility in size, and its convenience with stand-alone systems in
addition to grid-connected ones where they can be installed close to load centres, saving transmission lines losses [2-3]. Although
PV energy has recently received considerable attention, high installation cost and low conversion efficiency of PV systems set a
difficulty against its use on a large scale [4]. Furthermore, the non-linear behaviour and dependency of PV panels on the atmospheric
temperature and irradiance level create one of the main challenges facing the PV sector’s penetration to the energy market [5]. To
minimize these drawbacks, PV operation at the maximum power point is a necessity which in turn maximizes the PV system
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efficiency. Various MPPT techniques have been presented in literature [6-9].They differ in the tracking accuracy, convergence
speed, dynamic response under sudden environmental changes, required sensors, hardware implementation, and dependency on PV
module parameters.
The most commonly used MPPT algorithms are perturb and observe (P&O) and incremental conductance (Inc.Cond.) methods
[10]. P&O algorithm is widely used in PV stand-alone systems for its simple implementation [11-14]. In these PV systems, MPPT
algorithms are preferably realized using low cost microcontrollers in order to cut down the entire system cost. Thus, the P&O, being
an arithmetic-division-free algorithm, is a convenient choice to be implemented by these controllers. On the other hand, Inc.Cond. is
more complex in structure than P&O as it inhibits many mathematical divisions which increase the computational burden [15].
However, regarding these techniques performance, P&O can easily lead to erroneous judgment and oscillation around the maximum
power point (MPP) which results in power loss [16]. Hence, Inc.Cond. technique is a better candidate especially during rapidly varying
environmental conditions. This is because, when compared to P&O method, Inc.Cond. can accurately track the MPP, with less steady-
state oscillations and faster response during changes thus increasing the tracking efficiency [17-21].
In addition, many modifications have been introduced to fixed step-size used in the Inc.Cond. method to change it to a variable
one that gets smaller towards the MPP [22-28]. The latter improves the technique performance and solves the trade-off between
tracking accuracy and convergence speed. However, conventional variable step-size, automatically adjusted according to the PV
power change with respect to PV voltage change (∆P/∆V), can affect the MPPT performance due to the digression of this step size,
particularly under sudden changes [29, 30].
This paper aims at combining the advantages of simple algorithm structure with high system performance during transients in one
MPPT technique. Hence, a modified Inc.Cond. algorithm is proposed featuring full elimination of the division calculations thus,
simplifying the algorithm structure. In addition, a variable step-size is proposed which only depends on the PV power change (∆P),
thus eliminating its division by the PV voltage change (∆V). The proposed step-size can minimize power oscillations around the MPP
and effectively improve the MPPT dynamics during sudden changes. This will result in a total division-free variable-step technique
which does not only have the merits of enhanced steady-state and transient performance but also has simple algorithm implementation.
This reduces the processing real-time, enabling the algorithm to be implemented by low-cost microcontrollers which in turn reduces
system costs.
This paper is organized in eight sections. Following the introduction, the investigated PV system is presented. The following two
sections explain the conventional and the proposed Inc.Cond. techniques regarding their algorithm structure and the applied variable
step-size. The simulation and experimental results, which verify the superiority of the proposed technique over the conventional one,
are illustrated in the fifth and sixth sections respectively. An assessment is performed for the proposed MPPT technique under partial
shading conditions in the seventh section. Finally, a conclusion is presented in the eighth section.
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II. PV system under investigation
The considered PV system consists of a PV module, a DC-DC boost converter and a battery load as shown in fig. 1(a).
Duty cycle
PV module
Boost converter
Battery
loadV I
25 C
MPPT
Algorithm
CPV
L
CoVbattery
+
-
V
+
-Irradiance
IpvId
Rs
Rp
I
V
+
-
Ideal PV cell
Practical PV cell
(a) (b)
ISC
IMPP
VOCVMPP
Po
wer (
W),
Cu
rren
t (A
)
I-V
P-V
(CC )MPP
(CV )
Voltage (V)
dP/dV<0dP/dV>0dP/dV=0
(c)
0 5 10 15 20 250
50
100
150
Po
wer (
W)
Voltage (V)
Cu
rren
t (A
)
0
5
10
15P-V
I-V 25 C
40 C
15 C
0 5 10 15 20 25
Voltage (V)
0
50
100
150
Pow
er (
W)
Cu
rren
t (A
)
0
5
10
15P-V
I-V1000 W/m
2
700 W/m2
400 W/m2
(d) (e)
Fig. 1: PV system under consideration (a) Schematic diagram, (b) PV cell single diode model, (c) I-V and P-V characteristics at
given conditions, I-V and P-V curves of KD135SX_UPU PV module: (d) under three irradiance levels at 25C and (e) for three
different cell temperatures at irradiance of 1000 W/m2
A. PV mathematical model
A practical PV device can be represented by a light-generated current source and a diode altogether with internal shunt and series
resistances as shown in fig. 1(b). A PV module is composed of several PV cells and the observation of the characteristics at its
terminals results in expressing its output current by the following equation [31];
(1) 1expp
s
t
sopv
R
IRV
aV
IRVIII
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where V and I are the PV output voltage and current respectively. Ipv is the photovoltaic current which is generated by the incident
light (directly proportional to the sun irradiance) and Io is the saturation current of the PV module. a is the diode ideality constant
and Rs, Rp are the internal series and parallel resistances of the module respectively. Finally, Vt is the PV thermal voltage with Ns PV
cells connected in series. Vt equals to Ns.k.T/q where; q is the electron charge (1.60217646 × 10−19 C), k is Boltzmann constant
(1.3806503 × 10−23 J/ K), and T (in K) is the temperature of the p–n junction.
B. Boost converter
The design of boost converter, shown in fig. 1, can be summarized as follows [32];
)1( DVV battery
(2)
sw
LLf
VDi
(3)
where V is the PV output voltage, Vbattery is the battery load voltage and D is the duty ratio determined by the applied MPPT algorithm
to directly control the boost chopper switching. ∆iL is the change in inductor current, L is the chopper inductor and fsw is the chopper
switching frequency.
C. MPPT
Equation (1) shows that a PV module has non-linear I-V characteristics that depend on the irradiance level and PV cells'
temperature. Fig. 1(c) shows the I-V and P-V curves of a PV module, at a given cell temperature and irradiance level, on which it's
noticeable that the PV panel has an optimal operating point, the maximum power point (MPP). In the region left to the MPP, the PV
current is almost constant and the PV module can be approximated as a constant current (CC) source. On the other hand, right to the
MPP, the PV current begins a sharp decline and the PV module can be approximated as a constant voltage (CV) source. The PV
module characteristic curves vary with the changing irradiance level and cell temperature [5], as shown in fig. 1 parts (d) and (e).
The PV module short-circuit current is linearly dependent on the irradiance level unlike the open-circuit voltage which almost
independent of it. On the other hand, PV cell temperature significantly affects the open-circuit voltage value whereas it has a
negligible effect on the short circuit current value.
As the PV module characteristic curve shifts with changing irradiance or cell temperature, the MPP moves. Hence, continuous
tracking to the MPP becomes mandatory to maximize the PV system efficiency. The latter is achieved using an MPPT algorithm
which determines the appropriate duty ratio (D) that controls the switching of the DC-DC converter placed between the PV module
and the load to ensure that the PV panel maximum power is extracted. A successful MPPT technique compromises between the
tracking speed and steady-state accuracy and shows fast response during sudden environmental changes. According to these criteria,
the Inc.Cond. technique can be considered as an appropriate candidate [17-21].
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III. Conventional variable-step incremental conductance technique
The structure of the conventional variable-step Inc.Cond. technique can be illustrated in the following two subsections;
A. Conventional Inc.Cond. algorithm
Inc.Cond. technique is based on the slope of the PV module P-V curve [6] where;
∆I/∆V=-I/V
∆V=0
Inputs: V(k), I(k)
∆I=I(k)-I(k-1)
∆V=V(k)-V(k-1)
∆I/∆V>-I/V
∆I=0
∆I>0
D(k)=
D(k-1)+∆D
I(k-1)=I(k)
V(k-1)=V(k)
Return
Yes
YesYes
YesYes
No No
No No
No
D(k)=
D(k-1)-∆D
D(k)=
D(k-1)-∆D
D(k)=
D(k-1)+∆D
Fig. 2: Inc.Cond. algorithm flowchart (a) conventional
(4) MPPat 0dV
dP
(5) MPP left to 0dV
dP
(6) MPP right to 0dV
dP
Since
(7) )(
V
IVI
dV
dIVI
dV
IVd
dV
dP
Then
(8) MPPat V
-I
V
I
(9) MPP left to V
-I
V
I
(10) MPP right to V
-I
V
I
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The MPP can thus be tracked by comparing the instantaneous conductance (I/V) to the incremental conductance (ΔI/ΔV) and
accordingly the voltage perturbation sign is determined till reaching the MPP [7]. The flowchart of the conventional Inc.Cond.
algorithm is shown in fig. 2(a). If the irradiance increases (decreases) i.e. PV current increases (decreases), the MPP moves to the
right (left) with respect to PV voltage. To compensate for this movement, the MPPT must increase (decrease) the PV module’s
operating voltage.
When compared to other simple, low cost MPPT algorithms as P&O [12], the main advantage of Inc.Cond. algorithm is that it can
determine the accurate direction to reach the MPP thus decreasing the steady-state oscillations and improving system response under
rapidly changing conditions [16-21]. However, regarding the algorithm structure, conventional Inc.Cond. algorithm includes a number
of division calculations and a relatively complex decision making process which in turn raises the need of a more powerful
microcontroller featuring higher clock frequency, larger memory and floating-point calculation capability, decreasing the possibility
of achieving a low cost system solution [15].
B. Conventional variable step-size
For a fixed-step Inc.Cond. algorithm, a smaller step-size slows down the MPPT while a larger one increases the steady-state
oscillations around the MPP. A solution to this conflicting situation is to have a variable step-size that gets smaller towards the MPP
in order to balance the competing aims of convergence speed and tracking accuracy. The conventional variable step-size depends on
the PV power change divided by the PV voltage change (∆P/∆V) [23]. For a direct control scheme which directly controls the converter
switching without external control loops, the considered step is the change in the converter duty ratio (∆D) as shown in (11).
)11( .)( 1 V
PNconvD
where;
∆P=P(k)-P(k-1) (12)
∆V=V(k)-V(k-1) (13)
∆D=D(k)-D(k-1) (14)
and N1 is the scaling factor tuned at the design stage to adjust the conventional step-size (∆D) to compromise between tracking
accuracy and its convergence speed.
IV. Proposed variable-step incremental conductance technique
An enhancement is introduced in the structure of the conventional Inc.Cond. algorithm to eliminate all its division computations
and simplify its implementation. Moreover, the conventional variable step is modified to improve its performance. The proposed step
size is used by the proposed division-free Inc.Cond. algorithm to directly control the converter switching.
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A. Proposed division-free Inc.Cond. algorithm
A modification is introduced to the Inc.Cond. algorithm in order to eliminate all the division computations in the algorithm. Using
(8) - (10), the following modifications can be implemented:
(15) MPPat 0
V
I
V
I
(16) MPP left to 0
V
I
V
I
(17) MPP right to 0
V
I
V
I
Unifying the denominators in (15) - (17) to V(∆V), this
denominator can be eliminated from the first equation as it is
equalized to zero whereas only V is eliminated from the
denominator of the other two equations as it is always positive and
its sign won't affect these equations. Thus, manipulating (18) - (20)
results in;
(18) MPPat 0)()( VIIV
(19) MPP left to 0)()(
V
VIIV
(20) MPP right to 0)()(
V
VIIV
Finally, in order to eliminate the division calculations, the
Inc.Cond. algorithm rules can be rewritten as follows:
(𝑽 ∆𝑰) + (𝑰 ∆𝑽) = 𝟎 at MPP (21)
(𝑽 ∆𝑰) + (𝑰 ∆𝑽) > 0 && ∆𝑽 > 0 left to MPP (22)
(𝑽 ∆𝑰) + (𝑰 ∆𝑽) > 0 && ∆𝑽 < 0 right to MPP (23)
(𝑽 ∆𝑰) + (𝑰 ∆𝑽) < 0 && ∆𝑽 > 0 right to MPP (24)
(𝑽 ∆𝑰) + (𝑰 ∆𝑽) < 0 && ∆𝑽 < 0 left to MPP (25)
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Inputs: V(k), I(k)
∆I=I(k)-I(k-1)
∆V=V(k)-V(k-1)
∆V=0
V(∆I)+I(∆V)=0
V(∆I)+I(∆V)> 0
∆I=0
∆I>0
I(k-1)=I(k)
V(k-1)=V(k)
Return
Yes
YesYes
YesYes
No No
No No
No
∆V>0∆V>0
No
YesYes
No
D(k)=
D(k-1)+∆DD(k)=
D(k-1)-∆D
D(k)=
D(k-1)-∆D
D(k)=
D(k-1)+∆D
D(k)=
D(k-1)-∆D
D(k)=
D(k-1)+∆D
The flowchart of the proposed algorithm is given in fig. 2(b) where the removal of all the division computations in the algorithm
is compensated by applying arithmetic/logic mathematical operations. Thus, algorithm structure complexity is minimized which in
turn reduces processing real-time and enables the algorithm to be implemented by low cost microcontrollers.
B. Proposed variable step-size
The conventional step-size presented in (11), being dependant on the change of the PV power with respect to PV voltage change,
exhibits dynamic performance deterioration during sudden irradiance changes. Furthermore, steady-state power oscillations
noticeably arise around the MPP. This can be explained as follows;
During stable environmental conditions
Because of unavoidable factors as measurement error, ripples and noise, the condition that (ΔI/ΔV) and (- I/V) to be exactly equal
would never be satisfied. Thus, the operating point won't settle exactly at the MPP. Instead, it oscillates around the MPP, changing
the sign of the increment after each ΔP measurement [19, 20]. It's clear, from fig. 3(a), that in the regions close to the MPP and right
to it (constant voltage region), the change in PV voltage (∆V) is too small resulting in large ∆P/∆V steps. Although, these large step-
sizes increase the tracking speed at start of PV operation, they can enlarge the steady-state power oscillations affecting the PV system
accuracy which in turn decreases the algorithm efficiency.
Fig. 2: Inc.Cond. algorithm flowchart (b) proposed
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During varying irradiance conditions
The conventional variable step may show poor transient performance during sudden irradiance changes. As shown in fig. 3(a),
when the irradiance changes from G1 to G2, there is a considerable power change (∆P) while the PV voltage change (∆V) is relatively
too small. Since the step-size depends on ∆P/∆V, this will result in a large converter duty ratio change (∆D) thus shifting the operating
point far away from the new MPP. Noticeable transient decrease in the PV power occurs and the algorithm takes longer time to reach
the new MPP. Consequently, the transient power loss will increase, decreasing the tracking efficiency.
In order to overcome the latter, this paper proposes a variable step-size which depends only on the PV power change (∆P). The
proposed step size is used by the MPPT algorithm to directly control the converter switching, thus it represent the change in the
converter duty ratio as shown in (26);
(26) .)( 2 PNpropD
where N2 is the scaling factor which is tuned at the design stage to adjust the proposed step-size to compromise between the tracking
accuracy and its convergence speed.
It's observable, from the PV module P-V curve, that the change in PV power (∆P) is small around the MPP and large away from
it. Thus, the step-size, which depends on ∆P, will be large away from the MPP and decreases around the MPP to compromise between
the steady-state power oscillations and the tracking speed. Unlike the conventional variable step which depends on two rippled
parameters (∆P and ∆V) and their division, the proposed variable step depends only on ∆P. Removing the division by ∆V, from the
step-size, adds more simplification to the algorithm and eliminates large step-size variations that occur at small PV voltage changes.
Although this may slow down the tracking process at the starting of operation, it minimizes the steady-state oscillations around the
MPP thus improving the tracking accuracy and efficiency. Furthermore, this reduces the shift of the operating point away from the
MPP during sudden irradiance changes which results in better transient performance with fast dynamic response and less transient
power loss.
For further explanation, an illustrative example is shown in fig. 3 parts (b) and (c). When the irradiance decreases from G1 to G2,
the operating point shifts from 'A' to 'B', resulting in a considerable ∆P due to PV current change (∆I) while ∆V is almost zero. In
order to reach the new MPP 'M', the MPPT algorithm must decrement the duty ratio D. Hence, the algorithm performance is affected
by the variable step adopted to achieve this decrement.
For the conventional ∆P/∆V dependent step, the almost zero ∆V will result in a large step-size that vastly decrements D and shifts
the operation to point 'C'. Hence, a noticeable transient power loss occurs and the algorithm takes long time to reach the new MPP
'M'.
For the proposed ∆P based step, the large step-size is avoided and D is decremented to shift the operating point to 'D' which is close
to the MPP 'M'. This will fasten the tracking process and reduce transient power loss.
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Voltage (V)
Po
wer
(W
)
∆V
∆PG1
G2
MPP
(a)
Pow
er (
W)
Voltage (V)
G1
G2
∆P
C
B
M
A
1V
PND
Voltage (V)
Pow
er (
W)
G1
G2
D B
A
M ∆P
3 PND 2
(b) (c) Fig. 3: Effect of irradiance change on MPP (a) peak PV power shift, MPPT performance adopting: (b) conventional ∆P/∆V based variable step, and (c) proposed
∆P based variable step
V. Simulation work
Simulation work has been carried out to compare the steady-state and transient performance of the conventional Inc.Cond. technique
applying the conventional ∆P/∆V dependent variable step-size with that of the proposed division-free Inc.Cond. method adopting the
proposed ∆P based variable step-size. This is performed under two step changes in irradiance levels (from 1000W/m2 to 400W/m2 at
0.2s then from 400W/m2 to 700W/m2 at 0.4s.), at 25 C. A KD135SX_UPU PV module is utilized with specifications given in
appendix. Moreover, the applied DC-DC boost converter parameters are given as follows:
Chopper inductance (L): 2.3 mH, Switching frequency (fsw): 15 kHz and Vbattery= 3×12 V
Condition
Variable-step
MPPT method
Transient Steady-state
Undershoot Settling
(% PPV ) time (s)
Oscillations
at MPP (W)
MPPT
efficiency
(%ζ)
Start-up Conv. (∆P/∆V) 84.96% 0.024 4.25 98.7%
Proposed (∆P) 60.15% 0.04 0.0125 98.7%
From to 21000 W/m
20 W/m40
Conv. (∆P/∆V) 66.63% 0.021 1.5 98.6%
Proposed (∆P) 43.67% 0.014 0.0025 99.94%
From 2400 W/m
20 W/mto 70
Conv. (∆P/∆V) 89.35% 0.022 3.5 98.3%
Proposed (∆P) 28.5% 0.01 0.022 98.4%
TABLE I. SIMULATION PERFORMANCE INDICATORS OF THE CONVENTIONAL
AND PROPOSED TECHNIQUES UNDER TWO STEP CHANGES IN IRRADIANCE
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(a) (a)
(b) (b)
(c) (c)
(d) (d)
Fig. 5: Simulation results of the modified Inc.Cond. method adopting
the proposed ∆P based variable step under varying irradiance (a)
Overall PV power with zoom at (b) Start-up (c) First step change, (d) Second step change
Fig. 4: Simulation results of the conventional Inc.Cond. method adopting the conventional ∆P/ ∆V based variable step under varying irradiance (a) Overall
PV power with zoom at (b) Start-up (c) First step change, (d) Second step
change
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Figures 4 and 5 show the performance of the conventional technique and that of the proposed one respectively during the
considered step changes in irradiance while Table I gives their steady-state and transient performance parameters. It can be concluded
that; under varying irradiance conditions, both techniques can successfully track the PV maximum power yet with different levels
of tracking accuracy, speed and transient undershoot.
Figure 4 parts (a-d) show transient and steady state performance of the conventional method at start-up, first and second
irradiance step changes respectively. The latter is repeated for the proposed technique as shown in fig. 5 parts (a-d). It's observable,
that the elimination of the division by ∆V in the proposed step-size has limited the large increase in the step thus minimizing the
steady-state oscillations around the MPP on the penalty of slower tracking speed at the beginning of PV system operation. However,
during sudden irradiance changes, the proposed variable step gives better transient performance and faster response.
Considering Table I, the MPP tracking time, acquired by the proposed technique, is reduced by 33.3% and by 54.55% of that
achieved by the conventional technique at the first and the second step changes respectively. Furthermore, the proposed step
succeeded in reducing the power undershoot by almost 24.8%, 23% and 60.85% of the maximum tracked PV power at 1000 W/m2,
400 W/m2 and 700 W/m2 respectively. Finally, the minimal steady-state power oscillations, encountered by the proposed technique,
enhance its MPPT efficiency when compared to that of the conventional technique. Tracking efficiency can be defined as the
percentage ratio of the tracked PV power by the considered MPPT algorithm at certain environmental conditions to the peak PV
power under same conditions.
(a) (b)
Fig. 6: Power tracking nature on module P-V curves for (a) Conventional technique adopting ∆P/ ∆V step, (b) Proposed division-free technique with ∆P step.
The 3-D fig. 6 parts (a) and (b) illustrate PV power, tracked by the conventional and the proposed techniques respectively, versus
PV voltage and time. These figures give more clarification on both techniques' tracking performance on the P-V curves of the PV
module during the considered step changes in irradiance. It's clear that the proposed technique exerts less steady-state power
oscillations around the MPP of each P-V curve relative to each irradiance level. Furthermore, it shows faster response during
irradiance changes with less power undershoot.
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For further verification of the superiority of the proposed technique under changes, both techniques are retested at fixed irradiance
of 1000W/m2 under two step changes in temperature (from 25 C to 40 C at 0.2s then from 40 C to 15 C at 0.4s.)
25 C
0 0.1 0.2 0.3 0.4 0.5 0.60
50
100
150
Time (s)
PP
V (W
)
40 C15 C
Conventional
Zone1 Zone2 Zone3
0 0.1 0.2 0.3 0.4 0.5 0.60
50
100
150
PP
V (W
)
Time (s)
25 C
40 C15 C
Zone1
Proposed
Zone2 Zone3
(a) (a)
0 0.02 0.04 0.06 0.08 0.10
50
100
150
Time (s)
25 CZone1
PP
V (W
)
130
132
134
0 0.02 0.04 0.06 0.08 0.10
50
100
150Zone1 25 C
PP
V (W
)
Time (s)
130
132
134
(b) (b)
0.2 0.22 0.24 0.26 0.28 0.30
50
100
Time (s)
PP
V (W
)
40 CZone2
125
126
127
0.2 0.22 0.24 0.26 0.28 0.30
50
100
PP
V (W
)
Time (s)
Zone2 40 C
125
126
127
(c) (c)
0.4 0.42 0.44 0.46 0.48 0.5
100
120
140
Zone3 15 C
PP
V (W
)
Time (s)
138
139
140
141
0.4 0.42 0.44 0.46 0.48 0.5
100
120
140
PP
V (W
)
Time (s)
15 CZone3
138
139
140
141
(d) (d)
Fig.7: Simulation results of the conventional Inc.Cond. method adopting
∆P/ ∆V based variable step under varying temperature (a) Overall PV
power with zoom at (b) Start-up (c) First step change, (d) Second step
change
Fig. 8: Simulation results of the proposed l Inc.Cond. method
adopting ∆P based variable step under varying temperature (a)
Overall PV power with zoom at (b) Start-up (c) First step change,
(d) Second step change
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TABLE II. SIMULATION PERFORMANCE INDICATORS OF THE CONVENTIONAL AND PROPOSED TECHNIQUES
UNDER TWO STEP CHANGES IN TEMPERATURE
Figures 7 and 8 show the performance of the conventional technique and that of the proposed one respectively during the
considered step changes in temperature while Table II gives their steady-state and transient performance parameters. It can be
concluded that; under varying temperature conditions, both techniques can successfully track the PV maximum power yet with
different levels of tracking accuracy, speed and transient undershoot.
Figure 7 parts (a-d) show transient and steady state performance of the conventional method at start-up, first and second
temperature step changes respectively. The latter is repeated for the proposed technique as shown in fig. 8 parts (a-d). It's observable,
that the elimination of the division by ∆V in the proposed step-size has limited the large increase in the step thus minimizing the
steady-state oscillations around the MPP on the penalty of slower tracking speed at the beginning of PV system operation. However,
during sudden temperature changes, the proposed step gives better transient performance and faster response.
Considering Table II, the MPP tracking time, acquired by the proposed technique, is reduced by 81.25% and by 36.67% of that
achieved by the conventional technique at the first and the second step changes respectively. Furthermore, the proposed step
succeeded in reducing the power undershoot by almost 25.4%, 97% and 23.87% of the maximum tracked PV power at 25 C, 40 C
and 15 C respectively. Finally, the minimal steady-state power oscillations, encountered by the proposed technique, enhance its
MPPT efficiency when compared to that of the conventional technique.
Hence, simulation results show that the proposed technique's steady-state and transient performances outweigh those of the
conventional one, owing to its applied ∆P-based variable step-size, yet with simpler implementation due the entire division
calculations elimination from its algorithm structure. This is done under sudden irradiance changes as well as under sudden
temperature changes which in turn verifies the effectiveness and superiority of the proposed variable-step Inc.Cond. technique under
different environmental changes.
Condition
Variable-step
MPPT method
Transient Steady-state
Undershoot (% PPV )
Settling
time (s)
Oscillations
at MPP (W) MPPT
efficiency
(%ζ)
Start-up Conv. (∆P/∆V) 85.4% 0.025 4.4 98.7%
Proposed (∆P) 60% 0.045 0.013 98.7%
From
25 C to 40 C
Conv. (∆P/∆V) 100% 0.04 1 99.68%
Proposed (∆P) 2.94% 0.0075 0.003 99.94%
From
40 C to 15 C
Conv. (∆P/∆V) 28.74% 0.03 2 99.45%
Proposed (∆P) 4.87% 0.019 0.005 99.83%
15
VI. Experimental work
The merit of division elimination, from the Inc.Cond. algorithm, mainly lies in simplifying its structure and enhancing its
performance when being implemented by low cost microcontrollers. To clarify the latter, an experimental rig employing ARDUINO
Uno board, based on low cost Atmega328 16-bit microcontroller, is set and tested.
The conventional Inc.Cond. technique, featuring several division computations and applying the ∆P/∆V step-size, as well as the
proposed division-free IncCond. method, adopting the ∆P step-size, are both implemented using ARDUINO Uno board. The
execution time for both schemes has to be measured in order to choose the most convenient sampling time. Hence, it is calculated
by programming a pilot pin to toggle during program execution and triggers a digital output. Figure 9(a) shows the program execution
time for the conventional technique which is 400 µs while fig. 9(b) shows that of the proposed technique which is 300 µs. It's clear
that the elimination of the many division calculations in the proposed algorithm decreases the execution time and consequently
simplifies the controller operation. However, for fair comparison, same sampling time is chosen for both techniques which is 450
µs (to exceed the larger execution time of the conventional algorithm).
A real-time comparison between the proposed Inc.Cond. technique and the conventional one is carried out to verify the
superiority of the former. This is carried out during fixed and changing environmental conditions as illustrated in the following
subsections.
A. Stable environmental conditions
First, the performance of both the conventional and proposed variable-step Inc.Cond. techniques, are tested under fixed
environmental conditions (800 W/m2 and 23 C). A KD135SX_UPU PV panel is employed. Figure 9 (c) shows the performance of
the conventional technique employing ∆P/∆V-based variable step-size while fig. 9 (d) shows that of the proposed division-free
technique applying ∆P-based step. The proposed step-size minimizes the steady-state oscillation around the MPP, thus maximizing
tracking accuracy.
16
Conventional
Program
start
Loop
return
Microcontroller execution time
Proposed
Microcontroller execution time
Program
start
Loop
return
50 µs/div 50 µs/div
(a) (b)
Conventional ∆P/∆V-based step-size Proposed ∆P-based step-size
1 s/div, ch1: 5 V/div, ch2: 2 A/div, chM: 20 VA/div 1 s/div, ch1: 5 V/div, ch2: 2 A/div, chM: 20 VA/div
(c) (d)
Figure 9: Experimental results (a) conventional technique execution time adopting ∆P/∆V step, (b) proposed technique execution
time adopting ∆P step, (c) conventional technique performance adopting ∆P/ ∆V step and (d) proposed division-free technique
performance with ∆P step, using KD135X-UPU panel under steady-state conditions (800 W/m2 and 23C).
B. Sudden changing irradiance conditions
In order to compare the transient performance of both techniques under sudden changes, a step change should be created.
This is not practical with roof-mounted PV panels as their surrounding environmental conditions are uncontrollable. Thus, the need
of PV module simulator to replace actual PV panel is mandatory. However, these simulators are expensive instruments and not always
affordable. Thus, a lower-cost way of simulating I-V and P-V curves similar in nature to those generated by a PV panel is applied in
[33]. This paper presents a simplified circuit which employs a variable resistance (Rs) in series with a variable voltage DC power
supply and the MPPT tracker (boost converter) is connected at its output. This circuit produces a P-V curve that exhibits a peak point
for the tracker to lock on. Changing the variable series resistance will result in another P-V change with a new MPP to track.
Similarly, a simplified PV simulating circuit is employed, in this paper, as shown in fig. 10(a). This circuit simulates the PV source
when exposed to sudden step change in irradiance. It consists of a DC power supply with constant voltage of 28 V and two parallel
resistances of 3.2 Ω each in order to represent Rs. When the switch S is on, the two resistances are in parallel and Rs is 1.6 Ω and this
gives a P-V curve of almost 120W peak power. When S is opened, Rs becomes 3.2 Ω and a step decrease in the current I occurs which
results in a step decrease in the power level to about 60W as shown in fig. 10(b).
17
Figure 11 parts (a) and (b) show the performances of the conventional and the proposed Inc.Cond. techniques respectively, under
a step decrease in the PV simulator power level (from 120W to 60W). It's clear that the ∆P/∆V step applied in the conventional scheme
exhibits more steady-state power oscillations around the MPP than those acquired by the proposed ∆P step-size employed in the
modified scheme. Meanwhile, when zooming around both schemes' transient response during the step-change, as shown in fig. 11
parts (c) and (d), the conventional step-size shows slower response with settling time (ts) equals to 400 ms which is four times that of
the settling time experienced by the proposed step (ts=100 ms).
(a) (b)
(c)
Fig. 10: Experimental setup (a) Low cost PV emulator schematic diagram, (b) P-V, I-V characteristic curves of PV simulating circuit for two
different values of Rs, and (c) test-rig photography
ARDUINO Uno board based on
Atmega328 microcontroller Batteries
(3×12V, 7Ah)
LV-25P voltage transducer
LA-55P current transducer
Power supplies
Gate drive
Boost converter
Programmable DC
power supply
Resistor bank
Low cost
PV emulator
18
(a) 500 ms/div, ch1: 5 V/div, ch2: 5 A/div, chM: 20 VA/div (b) 500 ms/div, ch1: 5 V/div, ch2: 5 A/div, chM: 20 VA/div
(c)100 ms/div, ch1: 5 V/div, ch2: 5 A/div, chM: 20 VA/div. (d)100 ms/div, ch1: 5 V/div, ch2: 5 A/div, chM: 20 VA/div.
(e) 500 ms/div, ch1: 5 V/div, ch2: 5 A/div, chM: 20 VA/div
(f) 100 ms/div, ch1: 5 V/div, ch2: 5 A/div, chM: 20 VA/div.
Fig. 11: Step change experimental results, using a PV emulator, at Tsampling=450 µs for (a) conventional technique adopting ∆P/ ∆V step, (b) proposed
division-free technique adopting ∆P step, (c) Zoom of fig. 11(a), (d) Zoom of fig. 11(b), Step change experimental results, using a PV emulator, at
Tsampling=350 µs for (e) Proposed division-free technique adopting ∆P step and (f) Zoom of fig. 11(e)
19
Thus, at the same sampling time, the proposed technique shows better performance due to its employed ∆P-based step-size.
However, since this division-free technique exhibits less processing time (300 µs), its performance can be retested at a sampling
time of 350 µs which is less than that adopted in the previous case. This improves the sampling rate which fastens system response
during changes. Fig. 11(e) shows the proposed algorithm performance during the step decrease in power level at a sampling time of
350 µs. A zoom around this step-change is given by fig. 11(f). The settling time (ts) of the proposed scheme, in this case, is 40 ms
which is less than half that exhibited by the same scheme applying 450 µsec sampling time shown in fig.11(d).
In conclusion, experimental results verify that the proposed step-size enhances system steady-state and transient performance
during changes. Meanwhile the division computations elimination reduces the program execution time enabling the user to improve
the sampling rate which introduces further enhancement to the technique response during transients. The test rig for the considered
system in this section is shown in fig. 10(c).
21
Table III: Comparison between the proposed technique, implemented by Atmega 328 microcontroller, and experimental
prototypes presented in recent publications
Work,
Publication
year
Power
rating
Converter
type
Switching
frequency
MPPT
Technique
Hardware
Programmed
platform
Accuracy-
Power
oscillations
Tracking
efficiency
Tracking
speed
Price of
programmer
[27] (2014) 80W Buck 100 kHz Inc.Cond. FPGA XC3S400 2.7W
(3.4%)
98.8% 2.5 ms $38.5
[9] (2013) 200 W Boost 50 kHz P&O-based
on PI
controller
DSP
TMS320F240
20W
(10%)
95% 20 ms $25.64
[34] (2012) 240W Buck-
boost
50 kHz Improved
PSO
DSP
TMS320F240
8W
(3.33%)
96.5% 40 ms $25.64
[35] (2014)
800W
Boost
-----------
Zero-
oscillation
adaptive
step P&O
Microcontroller
TI C2000
20W
(2.5%)
98.75%
1s
$24
[14] (2012) 1080
W
Buck 10 kHz
P&O DSP
TMS320F2812
20W
(1.85%)
97.9% 0.5s $23.32
[26] (2013) 1080
W
Buck 10 kHz
Inc.Cond. DSP
TMS320F2812
20W
(1.85%)
96.8% 0.5s $23.32
[36] (2011) 10W Buck 100 kHz Load-
current
based
MPPT
DSP
TMS320F28335
0.04W
(0.4%)
97% 80 ms $21.17
[37] (2011) 54 W Boost 25 kHz PI–P&O DSP
TMS320F28335
7W
(13%)
93% 1s $21.17
[38] (2012) 150W Buck ----------- Fuzzy -
based P&O
DSP
TMS320F28335
2W
(1.3%)
98.5% 1.5 s $21.17
[39] (2014)
210W
Boost
----------
Adaptive
P&O-fuzzy
MPPT
DSP
TMS320F28335
1W
(0.5%)
95.2% 20 ms $21.17
[25] (2011) 110W Boost 50 kHz Inc.Cond. Microcontroller
C515C
15W
(1.4%)
96.8% 0.5 s $19.6
[21] (2014) 40W DC/DC
converter
10 kHz TS fuzzy-
based
Inc.Cond.
Embedded
controller
dsPIC33fJ128M
C802
1W
(2.5%)
97.5% 2s $4.46
[40] (2014)
[28] (2015)
87W SEPIC 20kHz Modified
Inc.Cond.
Microcontroller
PIC18f4520
1.5W
(1.7%)
99 % 0.2s $4.26
[41] (2013) 250W flyback 40 kHz PI-
Inc.Cond.
Embedded
controller
dsPIC33FJ06GS
202
14 W
(5.6%)
97.2% 5 s $3.95
Proposed
120W
Boost
15 kHz
Modified
step-size
division-
free
Inc.Cond.
Microcontroller
Atmega328
4W
(3.33%)
98.33%
40 ms
$2.00
---------------------: not mentioned, controller prices checked On-Line from [42, 43] at the submission time.
21
The proposed MPPT technique, implemented by Atmega328 microcontroller, is compared with several experimental prototypes
presented in most recent publications, as shown in Table III. Obviously, when compared with low-price microcontrollers' prototypes
[21, 28, 40 and 41], the proposed algorithm gives faster MPPT during sudden changes. On the other hand, prototypes of faster
response [9, 27, and 39] employ much more expensive microcontrollers than that applied in the proposed work. Moreover, the
proposed prototype experiences one of the high tracking efficiencies of more than 98%. In addition, it shows low steady-state power
oscillations giving acceptable accuracy. Hence, being implemented by low-cost Atmega328 microcontroller, the proposed division-
free algorithm, with the modified step-size, achieves the best compromise between MPPT dynamic response, steady-state
performance and employed microcontroller cost. Consequently, its functionality is validated offering an economical efficient
solution for stand-alone PV MPPT.
VII. Partial shading assessment
This section investigates the performance of the proposed Incremental Conductance MPPT algorithm under partial shading operating
condition. Moreover, a comparison between the conventional and modified proposed Incremental Conductance MPPT algorithms
is carried in this section under partial shading conditions.
To test the modified Inc.Cond. MPPT technique, under partial shading conditions, two KD135SX_UPU PV modules are connected
in series with a bypass diode connected in shunt with each module as illustrated in Fig. 12(a). First, both modules operate at normal
conditions (at 1000 W/m2, 25oC), then at t=0.3s, one module is partially shaded (working at 700 W/m).
Ideally, in the first case the total maximum PV power is 270W, while during partial shading; maximum PV power is reduced to
200W. When comparing the conventional and modified MPPT techniques during the previous conditions, the following performance
results;
• As shown in Fig. 12(d), the conventional MPPT technique shows high steady-state power oscillations with tracking
efficiency of 96% and 90.5% during normal and partial shading conditions respectively. Moreover, during the change, settling time
is about 0.2s and the PV power under-shoot is almost 18.5%.
• On the other hand, in Fig. 12(e), the modified MPPT technique shows faster response with settling time of 0.1s and reduced
PV power under-shoot of 6.6%. Moreover, it almost eliminates steady-state PV power oscillations showing more accurate results
and higher tracked PV power. This results in much enhanced tracking efficiency of 99.7% and 94.3% during normal and partial
shading conditions respectively.
Hence, the modified division-free Inc.cond. MPPT technique, adopting the proposed variable step-size, shows enhanced steady-
state and transient response during partial shading conditions when compared to the conventional variable-step division-included
Inc.Cond. technique.
22
Duty cycle
PV module
Boost converter
Battery
loadV I
MPPT
Algorithm
CPV
L
CoVbattery
+
-
V
+
-
(a)
(b) (c)
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
140
160
180
200
220
240
260
280
Time
260 W
190 W
Two series PV modules
operating at 1000 W/m2
Two series PV modules, one
operating at 1000 W/m2 and
another partially shaded
ts= 0.2 s
PP
V
269.3 W
198 W
140
160
180
200
220
240
260
280
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Timets= 0.1 s
Two series PV modules
operating at 1000 W/m2
Two series PV modules, one
operating at 1000 W/m2 and
another partially shaded PP
V
(d) (e)
Fig. 12: assessment of proposed IncCond. MPPT algorithm under partial shading:
(a) system block diagram, (b) P-V characteristics under uniform irradiance, (c) P-V characteristics under partial shading, (e) output PV power
under sudden partial shading using conventional IncCond. MPPT, and (f) output PV power under sudden partial shading using proposed IncCond.
MPPT
23
VIII. Conclusion
In this paper, a low-cost variable-step MPPT technique is proposed based on Inc.Cond. algorithm. The modified algorithm
features full elimination of the involved division computations, which simplifies its structure and reduces the required real processing
time, thus facilitating algorithm implementation by low-cost microcontrollers in order to cut down system costs. Furthermore, the
proposed associated variable step, being solely dependent on PV power change, shows minimal steady-state power oscillations
around the MPP in addition to improved transient performance under sudden changes. The effectiveness of the proposed technique
is verified by simulation and experimental results.
Appendix
)SCnINominal Short Circuit Current ( 8.37 A
)OCnVNominal Open Circuit Voltage ( 22.1 V
)MPPIMaximum Power Current ( 7.63 A
)MPPVMaximum Power Voltage ( 17.7 V
)maxPMaximum Output Power ( 135 W
)iKCurrent /Temp. Coefficient ( 3-5.02e CoA/
)vKVoltage/Temp. Coefficient ( 2-8e- CoV/
Series Cells 36 ----
TABLE IV. KD135SX_UPU MODULE SPECIFICATIONS AT 25OC, 1000 W/m2
24
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